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Electronic Colloquium on Computational Complexity

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Reports tagged with Lasserre:
TR13-105 | 29th July 2013
Raghu Meka, Avi Wigderson

Association schemes, non-commutative polynomial concentration, and sum-of-squares lower bounds for planted clique

Revisions: 1

Finding cliques in random graphs and the closely related ``planted'' clique variant, where a clique of size t is planted in a random G(n,1/2) graph, have been the focus of substantial study in algorithm design. Despite much effort, the best known polynomial-time algorithms only solve the problem for t = ... more >>>

TR14-118 | 9th September 2014
Albert Atserias, Massimo Lauria, Jakob Nordström

Narrow Proofs May Be Maximally Long

We prove that there are 3-CNF formulas over n variables that can be refuted in resolution in width w but require resolution proofs of size n^Omega(w). This shows that the simple counting argument that any formula refutable in width w must have a proof in size n^O(w) is essentially tight. ... more >>>

TR15-053 | 7th April 2015
Massimo Lauria, Jakob Nordström

Tight Size-Degree Bounds for Sums-of-Squares Proofs

We exhibit families of 4-CNF formulas over n variables that have sums-of-squares (SOS) proofs of unsatisfiability of degree (a.k.a. rank) d but require SOS proofs of size n^{Omega(d)} for values of d = d(n) from constant all the way up to n^{delta} for some universal constant delta. This shows that ... more >>>

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